Stability and robustness of discrete event dynamic systems

In this paper, the general concepts of stability of discrete event dynamic systems are defined and investigated. We present the stability in the sense of Lyapunov with resiliency, by incorporating the Lyapunov stability concepts (Michel and Miller 1977, Passino et al. 1994) with the concept of stability in the sense of error recovery (Ozveren and Willsky 1991a). We also provide algorithms for verifying stability and obtaining the domain of attraction. Upon the proposed stability concepts, we address the issue of robust stability and stabilizability. We assume that the plant G is not known exactly but we only know that it belongs to a set of models. In robust stability, we analyse the stability of the common invariant states set of all possible plant models. Then we derive the necessary and sufficient conditions for the robust stabilizability, i.e. the existence of a supervisor which makes the uncertain system robustly stable.